1 Analysis of J2K output
The model was run from the 01.01.1974 until the 31.12.2022.
2 Data availability of reference stations
3 Visual comparison of J2K, AquiFR and ADES
The data was normalized to a range between 0 and 1:
\[ norm(value)=\frac{value-min(value)}{max(value)-min(value)} \] Since the J2K groundwater component is only conceptual and the interest of the analysis lies more on the dynamics and not on the absolute values, the normalized values (norm(value)) were rescaled around the mean value: \[ resc(value) = \frac{norm(value)}{mean(norm(value))} \] For all stations, the starting time was set to the first hydrological year with more than 90% available data. In general, however, a warm-up period of 10 years was considered.
3.1 Time series
3.2 Regime
3.3 Duration curves
3.3.1 Interquartile range
The interquartile range (IQR) is the range between the 25th and 75th percentile, indicating the slope of the duration curve.
4 Goodness-of-fit tests
| Variable | Min | 1st Qu. | Median | Mean | 3rd Qu. | Max |
|---|---|---|---|---|---|---|
| Corr | 0.18 | 0.46 | 0.66 | 0.61 | 0.78 | 0.87 |
| KGE | -0.72 | 0.026 | 0.26 | 0.25 | 0.59 | 0.85 |
| NSE | -4.5 | -0.99 | -0.075 | -0.61 | 0.36 | 0.75 |
| mse | 0.068 | 0.17 | 0.22 | 0.28 | 0.32 | 0.94 |
| rmse | 0.26 | 0.41 | 0.47 | 0.5 | 0.56 | 0.97 |
| Variable | Min | 1st Qu. | Median | Mean | 3rd Qu. | Max |
|---|---|---|---|---|---|---|
| Corr | 0.034 | 0.44 | 0.66 | 0.59 | 0.78 | 0.94 |
| KGE | -6.4 | 0.0023 | 0.24 | -0.02 | 0.58 | 0.93 |
| NSE | -62 | -1.1 | 0.0069 | -2.6 | 0.24 | 0.87 |
| mse | 0.058 | 0.14 | 0.24 | 0.31 | 0.39 | 1.1 |
| rmse | 0.24 | 0.37 | 0.49 | 0.52 | 0.62 | 1 |
4.1 Maps
5 Correlation of the different plots
6 Comparison of different normalization approaches
6.1 Normalization with percentiles and median
Another approach to normalize the data is to use the 25th and 75th percentile instead of the minimum and maximum. After that the data is rescaled around the median.
\[ norm(value)=\frac{value-25Percentile(value)}{75Percentile(value)-25Percentile(value)} \]
\[ resc(value) = \frac{norm(value)}{median(norm(value))} \]
6.1.1 Time series
6.1.2 Regime
6.2 Normalization with percentiles
Only the normalization with percentiles but no rescaling.
6.2.1 Time series
6.2.2 Regime
6.3 Normalization with percentiles and mean
Normalization with percentiles but rescaling around the mean.
6.3.1 Time series
6.3.2 Regime
6.4 Z-score normalization
Z-score of a value is calculated with the mean (\(\mu\)) and the standard deviation (\(\sigma\)): \[ norm(value) = \frac{value - \mu}{\sigma} \] This is also the same normalization used for the calculation of the Standardized Precipitation Index (SPI) or the Standardized Piezometric Level Index (SPLI or IPS in french). The SPLI was calculated in the Explore2 project for the output of the model AquiFR and the reference data, and the model was evaluated using the NSE.
6.4.1 Time series
6.4.2 Regime
6.5 Normalization with the minimum and maximum of overlapping period
Same approach as the initial one, but not with the all time minimum and maximum but rather the minimum and maximum of the time period greater then the 50th quantile of the whole time period.